Cavanagh & Kram (1990) found height 6.8% in the variation of stride length in distance runners.
Good call. See pubmed for an abstract from the same authors where they indicate that At a given speed, the correlation coefficients between the subjects' anthropometric variables (APV) (such as stature, leg length, and limb segment mass) and their preferred stride variables were consistently low (less than or equal to 0.36) and not significantly different from zero.
There are stereotypes and "ideals" in every sport and there are almost always exceptions. Be the exception.
There are stereotypes and "ideals" in every sport and there are almost always exceptions. Be the exception.
Not sure what you're talking about. My argument in this dicussion is that tall people don't take longer strides but I am NOT arguing that tall guys can't run fast (see Jack Bacheler). So the stereotype of long striding tall runners is a myth. BTW, it's also a stereotype I personally defy -- I am 6ft and have very rapid turnover.
gigantic tall big guy huge wrote:
Haha, what are you talking about? The package does the tests, though it's such a simple regression it could be done without recourse to any computer or even a calculator.
The no-intercept model is correct because the original equation was stride length = 0.964 + 0.694 height. In other words, if you had an athlete of zero height, he would have a stride length of 0.964m.
The test is simple but still can be used wrongly. By forcing the regression line through the origin (no intercept) you are saying the modelmust include the point (0,0). The bulk of the data is around the point (2.2, 1.8), so a no intercept model must produce a line of best fit between that fits (0,0) and a few points around (2.2, 1.8), those points are pretty far apart (plot them and see, with axis of equal length, then draw a line from the origin. Does that line fit the data well? Plot the residuals, is there a pattern?) Didn't your p-value of less than 0.0001 look suspicious? That implies a perfect fit, don't think anything in nature is that perfect.
Since we are all athletics nerds here not Satistics/math nerds we will get back to the point in hand. As a side note I plotted the data and fitted a line and there seems to be a relationship (stronger than the one you got, maybe slightly different data), so yes there is a relationship between the stride length and height of the athletes in the Olympic final.
Can the results be applied to the general population (leaving out any stats concerns here)?
I think yes to an extent.
The general population is more or less of the same height.
However they are not of the same condition. Olympic finalist are stronger, fitter, more flexiable??? So would could a 12s 1.75m athlete achieve the same stride length, probably not. So other limiting factors may result in no relationship for 12s athletes. Since the athletes in the Olympic final all have more or less the same condition, the difference may have been due to differences in leg length, allowing greater distnace to be cover in the groubd contact phase (not flight phase). This assumes that joint angles are the same. Can we assume this, I think this would be wrong.
Can the results be applied to the other distances?
Here I think not, results from sprint races should not be applied to distance races. Sprinting is maximizing all factors (more or less) while the aim of distance running is to minimize metabolic cost for a given speed.
So who is faster tall or small?
The more the distance goes to sprints the more it will tend toward the taller, greater potential for a longer stride.
So for distance races?
We all can give examples of both tall and small that are great. Your height does not determine distance running performance, your cardovasular system does. Yes a taller person will have a bigger heart and lungs but will have to move a bigger body, that I think is where the difference lies. So if two athletes have the same engine but diiferent chassis which is better. Since running is weight bearing, the aim is to have the lightest body to move (hence skinny athletes), the increase in height is disportional to the weight (1.1????), so taller people are heavier. You could expect longer legs need fewer strides (not true but different debate), but it also take more energy to move long legs, so the greater stride rate may be not be as costly as you would expect (which is more costly to increase, interesting but different debate). So holding everything else the same I think it is better for distance runners to be small. A trunk has a big engine, big wheels to turn (longer radius of rotation or "stride") but not as fast as a sports car with a smaller engine, why? A sports car has less weight to move.
Koroibos wrote:
The test is simple but still can be used wrongly. By forcing the regression line through the origin
I'm not forcing the line through the origin. Points close to 0,0 will never, ever arise.
The bulk of the data is around the point (2.2, 1.8)
Which is why the regression line doesn't need to go anywhere near the origin or the x-axis.
a line of best fit between that fits (0,0) and a few points around (2.2, 1.8)
The point (0,0) doesn't exist and can't exist. There's no point in fitting a line to it, through it or close to it.
Didn't your p-value of less than 0.0001 look suspicious? That implies a perfect fit, don't think anything in nature is that perfect.
The p-value is the area under the curve of the corresponding distribution, in this case the F. A low p-value doesn't imply collinearity. R squared does that. If the data looks collinear remember the sample size.
So would could a 12s 1.75m athlete achieve the same stride length, probably not.
Compare like with like. Would your average joe of 1.75m have as long a stride as your average john 1.88m?
Can the results be applied to the other distances?
Here I think not, results from sprint races should not be applied to distance races.
Sprinting speed was not taken into account when the regression was done. There is a roughly linear relationship between height and stride length.
Height does not determine distance running performance
Agreed there. But that was never my quibble. My argument stemmed from the original poster who posited that smaller athletes have a greater power-to-weight ratio, for which there is no evidence.
Since running is weight bearing, the aim is to have the lightest body to move (hence skinny athletes), the increase in height is disportional to the weight (1.1????), so taller people are heavier.
Agreed again.
gall tuge hig bigantic guy wrote:
I'm not forcing the line through the origin. Points close to 0,0 will never, ever arise.
The p-value is the area under the curve of the corresponding distribution, in this case the F. A low p-value doesn't imply collinearity. R squared does that. If the data looks collinear remember the sample size.
A no intercept model does force it throught the origin.
The p-value is the probability of rejecting the null hypoth, they are probability curves. Collinearity is if two or more indepentant variables are correlated (say height and mass), I assume you meant linearity, you are right about the R sq but the p-value refers to the prob it differs from zero, hence a measure of strenght, lower P higher r.
"Can the results be applied to the other distances?
Here I think not, results from sprint races should not be applied to distance races."
Sprinting speed was not taken into account when the regression was done. There is a roughly linear relationship between height and stride length.
The aim of sprinting is different to that of distance running, different skills, so that is why you can use the study to mentioned for distance running, where other factors come into play, is is best to use longest stride in distnace running??
As for power to weight, smaller have advantage, as hieght increase so does weight, much is from muscles that can contribute to power but much is from bone, skin and other organs that can't. Tall people may be drawn to power sports (football etc) where strength training is undertaken resulting in tall people being observed with higher ratio, in theory small people should have.
stop already!
you guys are crushing any desire I have for running cause I'm 5'4" 122 pounds and I can't run like you say I should...
bwwaaaaaa
Lets look at the facts.
Yes - there are exceptional 'tall guys' (and tall in distance running would be 5ft11inches and over) who have made their mark on the track - (Bob Kennedy, Culpepper, Tahri, Tergat, and the Dutch guy - who is 6feet2inches - who has run around 27:20 for 10.000 - sorry forgot his name)....but those tall guys (sorry forgot to include Mottram) - there are dozens and dozens and dozens of shorter guys who are at the front.
The short guys have advantages that the tall guys don't have, such as lower weight, better biomechanics (in general, and most important of all - the energy cost of moving 'short levers' (legs and arms) is lower than the cost to move 'long levers' (long legs and arms).
In every sport where speed and flexibility are the rule (soccer, point guards in basketball, hockey players, etc...) the shorter guys dominate, because of their basic morphological advantages which have been stated above.
You will have a few tall guys in there, but never the numbers in comparison with the short guys who are dominating the sport of distance running.
It is all about biomechanics, energy costs, and efficiency, and in all those areas the short guys are at an advantage. The short guys may not have highest VO2's than some of the tall guys, but they (the shorties) are usually able to cover long distances at high speeds in a more efficient and less energy consuming way in comparison with their taller counterparts.
So, it is not just a question of VO2 Max, because if that were the case then you would have Nordic skiers running world beating times on the road and tracks, and this is not the case, and when they race on the roads and tracks, their times are often honorable but not world beating.
Many world class cross country skiers are around 6ft to 6ft3inches tall, with weights around the 165-180 mark, and the extra weight does not hurt them, because that extra weight is made of muscle, of which they (the nordic skiers) have a lot (in comparison with pure distance runners) of. But nordic skiing is a 'power technique' sport, and the extra muscle helps the skiers to have great propulsion from their poles. A guy like Tergat would be lost on skis, because of lack of basic muscle power and lack of technique. They had a Kenyan elite runner convert to cross country skiing (in Finland) a few years ago, and the Kenyan trained for two years, but his results were very poor, and he finished at the back of a World Nordic skiing race...
Most of these skiers (the elite world level guys) have among the highest VO2max rates of any athletes in all sports, but they are not able to run so fast on the track, because of their height, weight, and relative lack of efficient form (in running) compared with tiny Kenyans, Ethiopians and Moroccans.
Koroibos wrote:
A no intercept model does force it throught the origin.
The line can be extrapolated for a certain distance, but not to a point that does not or cannot exist. So saying I am forcing the line through (0,0) has no meaning. A regression line is fit to the data. The point (0,0) cannot exert any influence on the regression line.
The p-value is the probability of rejecting the null hypoth, they are probability curves.
The p-value is also the area under the probability curve.
Collinearity is if...
The all the data points fall on, or very close to, a straight line.
"Collinearity means that within the set of IVs, some of the IVs are (nearly) totally predicted by the other IVs."
I assume you meant linearity...
"Linearity is the assumption that there is a straight line relationship between variables." This is not the same as all the points falling on a straight line.
So my point was that the p-value doesn't imply collinearity; it implies that there is a low probability that a point will be found far from the regression line, i.e. linearity.
As for power to weight, smaller have advantage, as hieght increase so does weight, much is from muscles that can contribute to power but much is from bone, skin and other organs that can't. Tall people may be drawn to power sports (football etc) where strength training is undertaken resulting in tall people being observed with higher ratio, in theory small people should have.
In events where the requirement is for highest PTW ratio, say 100m or even 60m, there is no evidence that it is dominated by small guys. The average height of world class sprinters is greater than the average height of the general population. There is no evidence for your claim that "smaller have advantage". (Note: I'm not even claiming that taller people have advantage in the PTW ratio stakes.)
guge gall gig gigantic guy wrote:
Koroibos wrote:A no intercept model does force it throught the origin.
The line can be extrapolated for a certain distance, but not to a point that does not or cannot exist. So saying I am forcing the line through (0,0) has no meaning. A regression line is fit to the data. The point (0,0) cannot exert any influence on the regression line.
Collinearity is if...
The all the data points fall on, or very close to, a straight line.
"Collinearity means that within the set of IVs, some of the IVs are (nearly) totally predicted by the other IVs."
If you fit a no-intercept model, the model will return zero (y) if you enter zero as the indepentant variable (x). So the regression line will go through zero, where the other points are determines the slope of the line. Your statement that the line can only be extrapolated for a certain distance is correct. However, it negates your rational for using the no intercept model, entering zero as the independant variable (IV) would return a non-zero dependant variable (DV) which does not make sense.
The p-value refer to the test that the slope differs from zero, a regression model that goes through the origin and non-zero points must have a non-zero slope. If you don't believe the line goes through the origin, put zero in and see what you get out.
A regression line is a model for explaining the variation in the dependant variable (DV) normally "y" by the variation in the indepentant variable (IV) normally called "x". So a bivariate regression equation is
y = a + b.x. However, regression can be used with more than one IV, with a equation y = a + b1.x + b2.z + b3.w. So you have a set of IV that can be used to explain the variation the the DV. However, there may be significant correlation between IV, so the variation in one IV may explain the variation in another, so the entry of one IV into the model cause the other IV not to explain any additional variability in the DV, so will not be included and other problems can arise. Now re-read your definition of collinearity.
Koroibos wrote:
If you fit a no-intercept model, the model will return zero (y) if you enter zero as the indepentant variable (x).
I'm getting confused. The regression equation is used to predict y-values, correct? By entering valid x-values, correct? So what are valid x-values? In the context?
Your statement that the line can only be extrapolated for a certain distance is correct. However, it negates your rational for using the no intercept model, entering zero as the independant variable (IV) would return a non-zero dependant variable (DV) which does not make sense.
Of course it doesn't. Who, in their right mind, would enter zero for the IV?
The p-value refer to the test that the slope differs from zero, a regression model that goes through the origin and non-zero points must have a non-zero slope. If you don't believe the line goes through the origin, put zero in and see what you get out.
Again, it doesn't and can't go through the origin. You can only substitute in valid predictor values, and anything less than about 1m is invalid. (We are talking about heights of human beings here, not just x's)
Now re-read your definition of collinearity.
Perhaps you misunderstood my definition of it. Here's what I said:
"The p-value is the area under the curve of the corresponding distribution, in this case the F. A low p-value doesn't imply collinearity [perfect fit]. If the data looks collinear [perfect] remember the sample size."
A low p-value implies linearity, not collinearity. Linearity is a linear relationship between predictors and responses; collinearity is "a perfect fit", with all the points falling on a straight line. Linearity allows for some small variance from the regression line. Collinearity doesn't.
Not sure if this is wind-up, so will so will just clear up some of the questions you asked, if you really don't understand.
big buge bigantic ball buy wrote:
I'm getting confused. The regression equation is used to predict y-values, correct? By entering valid x-values, correct? So what are valid x-values? In the context?.
stride length (y) = [a +] b.height (x)
valid values strictly speaking are from the small height in the sample to the largest, but the model could be used 20cm either side I expect. However, by fitting a no intercept model you made the line go through the origin even though it was not used in the calculation, put zero in to the regression equation you got and see. It is a straight line. Plot the data and see if an intercept model or not fits better, and as you said it should not be used to predict y values when non-valid x values are entered, so the fact it cross the y-axis at a non-zero stride length is not a problem.
Of course it doesn't. Who, in their right mind, would enter zero for the IV?
Again, it doesn't and can't go through the origin. You can only substitute in valid predictor values, and anything less than about 1m is invalid. (We are talking about heights of human beings here, not just x's)
Yes it would be wrong to enter zero BUT if you did it would return zero, so the model may not predict the other values well as it ALSO equals zero when zero is entered. Since neither (intercept or no-intercept) model would be used with very small heights, which fits the data best? least residuals? The intercept model is free to cross the y-axis at any point, the no-intercept model MUST cross at zero. However, both should be only used in the range of valid values, so the fact one will return a non-zero when zero is entered is not a problem.
"Now re-read your definition of collinearity."
Perhaps you misunderstood my definition of it. Here's what I said:
...collinearity is "a perfect fit", with all the points falling on a straight line. Linearity allows for some small variance from the regression line. Collinearity doesn't.
I was refering to the other definition of collinearity you gave. "Collinearity means that within the set of IVs, some of the IVs are (nearly) totally predicted by the other IVs." See what I said in my last post about more than to indepedant variable (IV)(or can be called predictor variables in this case height and weight predicting stride length). The "perfect fit" idea would be true if it said "Collinearity means the DV is (nearly) totally predicted by the IV." Collinearity is when the indepedant variables (IV) are correlated with another indepedant variable (or variablity in one explains variability in the other), not the dependant variable (y)or stride length in this case.
Hope that clears it up and you where not just joking with your questions.
I can see why you are getting confused with the definition of collinearity. Put it into google and read the first two or three defintions, see where you got your defintion from. Rememeber regression aims to explain the variance in the dependant variable (y) by the variance in the independant variable (IV), or in the case of more than one, variables (IVs) or a set of IV.
Koroibos wrote:
Not sure if this is wind-up, so will so will just clear up some of the questions you asked, if you really don't understand.
I understand perfectly. When to use an intercept model, and when to use a no-intercept model. Something you can't seem to grasp.
I repeat: The model is used to predict y-values. From valid x-values. Putting in zero as a predictor is nonsense.
Any no-intercept model will return zero if zero is entered, so are you saying every no-intercept model is wrong?
If you are, then why do statisticians use them? If you are not, then when is it correct to use one?
and the Dutch guy - who is 6feet2inches - who has run around 27:20 for 10.000 - sorry forgot his name)....
Kamiel Maase (13:13, 27:26, 2:08 marathon). He's very tall and makes a great windblock if you can keep up to him long enough.
basically, this thread is just an ego boost for the short guys because they can't get chicks or, when they do, can't satisfy them.
face it, if you're under 5'10" and you're not a movie star or sports hero, you've gotta settle for ugly or otherwise undesirable women.
that makes it a real nature-vs-nurture argument about the fast short runners: does being short make them naturally better runners? or does being short leave them with few options for happiness outside running? probably a little of both.
guy gigantic huge tall big wrote:
The p-value of 0.084 is too high to rejest the null hypothesis, but there's a problem with the model. The intercept is meaningless. So we run the analysis again without the intercept.
So why is the intercept a problem if zero is not a valid x-value? The no-intercept model does force the line (it is a line so extends after the the range of valid values) through the origin. The no intercept model is used where the range of valid values does converge towards zero and when x is zero y is zero. Such as mile per gallon v speed, or age v total number of heart beats (assuming they are linear).By setting a condition that the line must pass through the origin it makes it more restrictive than the intercept model. The intercept model with always fit the data as well as the no-intercept model.
hig huge hall higantic huy wrote:
I understand perfectly. When to use an intercept model, and when to use a no-intercept model. Something you can't seem to grasp.
I repeat: The model is used to predict y-values. From valid x-values. Putting in zero as a predictor is nonsense.
Any no-intercept model will return zero if zero is entered, so are you saying every no-intercept model is wrong?
If you are, then why do statisticians use them? If you are not, then when is it correct to use one?
You sound like your statistics knowledge is self-taught, which is admirable, that is a hard way to learn. I have a degree in Statistics, I tried to help you on some points but you don't seem to be able except anything. It is not good enough to read something, you also have to interpret it correctly. Thought I would just help you out, but have had enough of it now. More importantly this is a thread about tall and small runners.
elflord wrote:
Note there are no really really tall runners at national or world class levels, ever,
What's your definition of "really really tall" ? I'd say Jack Bacheler qualifies.
There are plenty of "exceptions" to this alleged rule besides Batcheler. I think Kirk Pfeffer would classify as being tall since he's 6'6 and was world class in the marathon.
I think there are lots of other elements that far out rank the importance of height in distance running performance. Having them in abundance will make you great, but there are still benefits to being tall or small, but it is so far down the list we see great runners that are both short and tall. Holding everything equal, I think it is better to be tall up to 800/1500 and shorter after.
Here is another question, is it better to be tall or small (6.2 or 5.7) in the steeplechase. Most would say tall as the hurdles are lower in relation the athletes height. However, as height increases so does weight, so the taller people have to carry around more weight for the 3000m. However, the tall people don't have to lift their center of mass as much as the smaller athletes when they hurdle, but have to lift a greater weight vertically, be that a shorter distance. So where is the trade-off between having to lift a smaller mass but a greater distance, and a greater mass a shorter distance, plus having to carry it round 7.5 laps (depending on where the water jump is). So does the taller athlete do more work or does the smaller?
Koroibos wrote:
So why is the intercept a problem if zero is not a valid x-value?
There are other meaningless values. Think of heights of human beings.
The no-intercept model does force the line (it is a line so extends after the the range of valid values) through the origin.
Well you just carry right on extending the line through the origin. I won't, and as stated earlier in the thread, my model agrees more closely with the models of other researchers:
Work conducted by Hoffman on male 100 metre sprinters (10.4 to 11.0 seconds) indicated that the average stride length was 1.14 times the athletes height. Similar work conducted by Rompotti on the best twelve 100m sprinters (11.0 to 12.4 seconds) at Stanford University concluded that the normal stride length was 1.17 times the athletes height. Despite the differences in abilities of the athletes in each group the results are fairly similar.
Further work conducted by Atwater on twenty three 100m sprinters (9.9 to 10.4 seconds) concluded that the average stride length was 1.35 times the athletes height.
No intercepts mentioned there. I wonder why? Perhaps because it's meaningless.
You sound like your statistics knowledge is self-taught, which is admirable, that is a hard way to learn. I have a degree in Statistics, I tried to help you on some points but you don't seem to be able except [sic] anything. It is not good enough to read something, you also have to interpret it correctly.
Well, you may have a degree, but it is not good enough just to learn stuff off by rote for an exam; you also have to interpret it correctly.
Merry Christmas
Terry